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Prove that the square of an odd number is always 1 more than a multiple of 4

(2n+1)²= (2n+1)(2n+1)
Use FOIL method= 4n²+2n+2n+1= 4n²+4n+1= 4(4n+n)+1
4n+n is just a number, therefore proved

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How to solve a quadratic by factorisation?

There are 4 different methods to solve quadratics: factorisation, quadratic formula, graphically and completing the square. Today we shall solve equations by factorisation.Using the equation x²...

Answered by Oyin O. • Maths tutor

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Prove algebraically that the straight line with equation x - 2y = 10 is a tangent to the circle with equation x^2 + y^2= 20

rearrange line equation: x=10 + 2ysubstitute into circle equation: (10+2y)² + y²=20expand: 4y² +20y +20y + 100 + y²= 20 collect terms: 5y² + 40y +100...

Answered by Annabel B. • Maths tutor

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Expand and simplify 6x^2(x-1)(x+2)

First we need to use the rules of BIDMAS (brackets, indices, division, multiplication, addition, subtraction)So we must deal with the brackets of the function first(x-1)(x+2)To expand these brackets we us...

Answered by Emily p. • Maths tutor

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